Subgroups — #12963988

Order 1280.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10618052	C₂	1	1	yes	maximal, characteristic
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614860	C₂	1	1	yes	maximal, characteristic, complemented
4	#10611689	C₂	1	1	yes	maximal, characteristic, complemented
5	#10611669	C₂	1	1	yes	maximal, characteristic, complemented
6	#10611649	C₂	1	1	yes	maximal, characteristic, complemented
7	#10611636	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
9	#10611249	C₂	1	1	yes	maximal, characteristic, complemented
10	#10611210	C₂	1	2	yes	maximal, complemented
11	#10611187	C₂	1	2	yes	maximal, complemented
12	D₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
13	#10611154	C₂	1	2	yes	maximal, complemented
14	#10611134	C₂	1	1	yes	maximal, characteristic, complemented
15	#10611134	C₂	1	2	yes	maximal, complemented
16	#10611105	C₂	1	2	yes	maximal, complemented
17	#10611100	C₂	1	2	yes	maximal, complemented
18	#10611065	C₂	1	1	yes	maximal, characteristic, complemented
19	#10611060	C₂	1	1	yes	maximal, characteristic, complemented
20	#10610288	C₂	1	2	yes	maximal, complemented
21	#10610279	C₂	1	2	yes	maximal, complemented
22	C₄×#4047	C₂	1	1	yes	maximal, characteristic, complemented
23	#10610178	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#529	C₂²	1	1	yes	characteristic
25	C₂×D₅×M₁₆	C₂²	1	2	yes	—
26	C₂×#4047	C₂²	1	1	yes	characteristic
27	C₂×#4047	C₂²	1	1	yes	characteristic
28	C₂²×#676	C₂²	1	2	yes	—
29	#66042	C₄	1	2	yes	—
30	#66039	C₄	1	2	yes	—
31	#66028	C₄	1	1	yes	characteristic
32	#66024	C₄	1	1	yes	characteristic
33	#66010	C₄	1	1	yes	characteristic
34	#66005	C₄	1	1	yes	characteristic
35	#65995	C₄	1	2	yes	—
36	#65993	C₄	1	2	yes	—
37	#65973	C₄	1	1	yes	characteristic
38	#65965	C₄	1	1	yes	characteristic
39	#65950	C₄	1	1	yes	characteristic
40	#65946	C₄	1	1	yes	characteristic
41	#65912	C₂²	1	1	yes	characteristic
42	C₄×#713	C₂²	1	1	yes	characteristic
43	#65891	C₂²	1	1	yes	characteristic
44	#65891	C₂²	1	2	yes	—
45	#65881	C₂²	1	2	yes	—
46	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
47	#65862	C₂²	1	2	yes	—
48	D₅×#117	C₂²	1	2	yes	—
49	C₄×#709	C₂²	1	1	yes	characteristic
50	C₄×#709	C₂²	1	1	yes	characteristic
51	C₅×#446	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×#436	C₂²	1	1	yes	characteristic
54	C₅×#435	C₂²	1	2	yes	complemented
55	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
56	C₅×C₈×D₄	C₂²	1	2	yes	complemented
57	C₅×#433	C₂²	1	2	yes	complemented
58	C₅×#432	C₂²	1	1	yes	characteristic, complemented
59	C₅×#405	C₂²	1	2	yes	complemented
60	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
61	#65417	C₂²	1	2	yes	—
62	#65416	C₂²	1	2	yes	complemented
63	#65411	C₂²	1	2	yes	complemented
64	#65400	C₂²	1	2	yes	—
65	#65400	C₂²	1	2	yes	complemented
66	#65400	C₂²	1	2	yes	complemented
67	#65400	C₂²	1	2	yes	complemented
68	#65390	C₂²	1	1	yes	characteristic, complemented
69	#65390	C₂²	1	1	yes	characteristic, complemented
70	#65390	C₂²	1	2	yes	complemented
71	#65313	C₂²	1	1	yes	characteristic, complemented
72	Q₈×#168	C₂²	1	1	yes	characteristic, complemented
73	#65301	C₂²	1	1	yes	characteristic
74	#65301	C₂²	1	2	yes	complemented
75	#65300	C₂²	1	2	yes	complemented
76	D₄×#168	C₂²	1	1	yes	characteristic
77	#65289	C₂²	1	2	yes	complemented
78	#65286	C₂²	1	2	yes	complemented
79	#65214	C₂²	1	1	yes	characteristic, complemented
80	C₄×#681	C₂²	1	1	yes	characteristic, complemented
81	#65128	C₂²	1	2	yes	—
82	#65128	C₂²	1	2	yes	—
83	#65127	C₂²	1	1	yes	characteristic
84	#65127	C₂²	1	1	yes	characteristic
85	#65127	C₂²	1	2	yes	complemented
86	#65126	C₂²	1	1	yes	characteristic
87	#65125	C₂²	1	2	yes	complemented
88	#65124	C₂²	1	1	yes	characteristic, complemented
89	#65124	C₂²	1	2	yes	complemented
90	#65122	C₂²	1	1	yes	characteristic, complemented
91	#65122	C₂²	1	2	yes	complemented
92	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	#65119	C₂²	1	1	yes	characteristic, complemented
94	#65119	C₂²	1	1	yes	characteristic, complemented
95	#65119	C₂²	1	2	yes	complemented
96	#65117	C₂²	1	2	yes	complemented
97	#65019	C₂²	1	2	yes	—
98	#65018	C₂²	1	2	yes	—
99	#65018	C₂²	1	2	yes	complemented
100	#65018	C₂²	1	2	yes	complemented
101	#65018	C₂²	1	2	yes	complemented
102	#65016	C₂²	1	2	yes	—
103	#65015	C₂²	1	2	yes	—
104	#65014	C₂²	1	2	yes	complemented
105	D₅×C₂²⋊C₈	C₂²	1	2	yes	—
106	#65009	C₂²	1	2	yes	complemented
107	#65009	C₂²	1	2	yes	complemented
108	#65009	C₂²	1	2	yes	complemented
109	#64998	C₂²	1	2	yes	complemented
110	#64997	C₂²	1	2	yes	—
111	#64997	C₂²	1	2	yes	—
112	#64996	C₂²	1	2	yes	complemented
113	#64996	C₂²	1	2	yes	complemented
114	#64995	C₂²	1	2	yes	complemented
115	#64994	C₂²	1	2	yes	complemented
116	#64990	C₂²	1	2	yes	complemented
117	#64978	C₂²	1	1	yes	characteristic
118	#64978	C₂²	1	1	yes	characteristic
119	#64978	C₂²	1	2	yes	—
120	#64978	C₂²	1	1	yes	characteristic, complemented
121	#64978	C₂²	1	1	yes	characteristic, complemented
122	#64977	C₂²	1	1	yes	characteristic
123	#64977	C₂²	1	1	yes	characteristic
124	#64977	C₂²	1	2	yes	complemented
125	C₄×#676	C₂²	1	1	yes	characteristic
126	C₄×#676	C₂²	1	2	yes	complemented
127	C₄×#676	C₂²	1	1	yes	characteristic, complemented
128	C₄×#676	C₂²	1	2	yes	complemented
129	#64974	C₂²	1	2	yes	complemented
130	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
131	C₄×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
132	#64968	C₂²	1	1	yes	characteristic, complemented
133	#64968	C₂²	1	1	yes	characteristic, complemented
134	#64968	C₂²	1	2	yes	complemented
135	#60217	—	5	1	no	maximal, Sylow
136	C₂×#713	C₂×C₄	1	1	yes	characteristic
137	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
138	C₂×#709	C₂×C₄	1	1	yes	characteristic
139	C₂×#709	C₂³	1	1	yes	characteristic
140	C₂²×C₄×D₅	C₂³	1	2	yes	—
141	C₂×C₅×M₁₆	C₂³	1	2	yes	—
142	C₂²×C₅×C₈	C₂³	1	2	yes	—
143	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₅×#126	C₂×C₄	1	2	yes	—
146	C₅×#125	C₂×C₄	1	1	yes	characteristic
147	C₅×#124	C₂×C₄	1	1	yes	characteristic
148	C₅×#123	C₂×C₄	1	2	yes	—
149	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
150	C₅×#121	C₂×C₄	1	1	yes	characteristic
151	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
152	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₄×C₅×D₄	C₂³	1	2	yes	—
154	C₅×#117	C₂³	1	2	yes	—
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	#4092	C₂×C₄	1	1	yes	characteristic
157	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
158	#4090	C₂×C₄	1	1	yes	characteristic
159	#4085	C₂×C₄	1	2	yes	—
160	#4084	C₂×C₄	1	2	yes	—
161	#4084	C₂×C₄	1	1	yes	characteristic
162	#4083	C₂×C₄	1	2	yes	—
163	#4082	C₂×C₄	1	1	yes	characteristic
164	#4082	C₂×C₄	1	2	yes	—
165	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
166	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
167	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
168	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
169	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
170	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
171	C₄×C₂²⋊D₅	C₂³	1	2	yes	—
172	C₄×C₂²⋊D₅	C₂³	1	2	yes	—
173	C₄×C₂²⋊D₅	C₂³	1	2	yes	—
174	#4072	C₂×C₄	1	1	yes	characteristic
175	#4072	C₂³	1	1	yes	characteristic
176	#4072	C₂³	1	2	yes	—
177	C₂×#681	C₂³	1	2	yes	—
178	C₂×#681	C₂³	1	1	yes	characteristic
179	C₂×#681	C₂³	1	1	yes	characteristic
180	C₂²×#168	C₂³	1	2	yes	—
181	D₅×M₁₆	—	2	8	no	—
182	#4047	—	2	4	no	—
183	#4047	—	2	4	no	—
184	C₂×#676	—	2	8	no	—
185	C₂×#676	C₂³	1	2	yes	—
186	C₂×#676	C₂³	1	2	yes	—
187	C₂×#676	C₂³	1	2	yes	—
188	C₂×#676	C₂³	1	1	yes	characteristic
189	C₂×#676	C₂³	1	1	yes	characteristic
190	C₂×#676	C₂³	1	1	yes	characteristic
191	C₂×#676	C₂³	1	2	yes	—
192	C₂×#676	C₂³	1	2	yes	—
193	C₂×#676	C₂³	1	1	yes	characteristic
194	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
195	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
196	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
197	C₂×C₈×D₅	C₂³	1	2	yes	—
198	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
199	#4044	C₂×C₄	1	2	yes	—
200	#4043	C₂×C₄	1	1	yes	characteristic
201	#4043	C₂×C₄	1	2	yes	—
202	#4043	C₂×C₄	1	1	yes	characteristic
203	#4042	C₂×C₄	1	2	yes	—
204	#4042	C₂×C₄	1	2	yes	—
205	#4042	C₂×C₄	1	2	yes	—
206	#4040	C₂×C₄	1	2	yes	—
207	#4040	C₂×C₄	1	2	yes	—
208	#4039	C₂×C₄	1	1	yes	characteristic
209	#4039	C₂×C₄	1	1	yes	characteristic
210	#4039	C₂×C₄	1	2	yes	—
211	#4038	C₂×C₄	1	2	yes	—
212	#4038	C₂×C₄	1	2	yes	—
213	#4038	C₂×C₄	1	1	yes	characteristic
214	#4038	C₂×C₄	1	2	yes	—
215	D₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
216	D₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
217	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
218	#4036	C₂×C₄	1	1	yes	characteristic
219	#4036	C₂×C₄	1	2	yes	—
220	#4035	C₂×C₄	1	2	yes	—
221	#4035	C₂×C₄	1	2	yes	—
222	#4034	C₂×C₄	1	1	yes	characteristic
223	#4031	C₂×C₄	1	2	yes	—
224	#4030	C₂×C₄	1	2	yes	—
225	#4030	C₂×C₄	1	2	yes	—
226	#4029	C₂×C₄	1	2	yes	—
227	#4029	C₂×C₄	1	2	yes	—
228	#4029	C₂×C₄	1	2	yes	—
229	#4029	C₂×C₄	1	2	yes	—
230	#4029	C₂×C₄	1	2	yes	—
231	#4028	C₂×C₄	1	2	yes	—
232	#4027	C₂×C₄	1	2	yes	—
233	D₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
234	D₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
235	D₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
236	#4025	C₂×C₄	1	2	yes	—
237	#4025	C₂×C₄	1	2	yes	—
238	#4025	C₂×C₄	1	2	yes	—
239	#4025	C₂×C₄	1	2	yes	—
240	#4024	C₂×C₄	1	2	yes	—
241	#4023	C₂×C₄	1	2	yes	—
242	#4023	C₂×C₄	1	2	yes	—
243	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
244	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
245	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
246	C₄×D₂₀	C₂³	1	1	yes	characteristic
247	C₄×D₂₀	C₂³	1	2	yes	—
248	#4018	C₂×C₄	1	2	yes	—
249	#4018	C₂³	1	1	yes	characteristic
250	#4018	C₂³	1	1	yes	characteristic
251	#4018	C₂³	1	2	yes	—
252	C₄²×D₅	C₂³	1	2	yes	—
253	C₄²×D₅	C₂³	1	1	yes	characteristic
254	C₄²×D₅	C₂³	1	1	yes	characteristic
255	C₄²×D₅	C₂³	1	2	yes	—
256	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
257	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
258	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
259	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
260	C₄×Dic₁₀	C₂³	1	2	yes	—
261	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₅×C₄⋊C₈	C₂³	1	2	yes	—
264	C₅×C₄⋊C₈	C₂³	1	2	yes	—
265	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₅×#97	C₂³	1	2	yes	—
269	C₅×#97	C₂³	1	2	yes	—
270	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
271	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
272	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
273	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
274	C₄×C₅×C₈	C₂³	1	2	yes	—
275	C₂²⋊#168	C₂³	1	2	yes	—
276	C₂²⋊#168	C₂³	1	2	yes	—
277	C₂²⋊#168	C₂³	1	2	yes	—
278	#3952	C₂³	1	2	yes	—
279	#3952	C₂³	1	2	yes	—
280	#3952	C₂³	1	2	yes	—
281	#3952	C₂³	1	2	yes	—
282	#3952	C₂³	1	2	yes	—
283	#3952	C₂³	1	2	yes	—
284	#3947	C₂³	1	1	yes	characteristic
285	#3947	C₂³	1	1	yes	characteristic
286	#3947	C₂³	1	2	yes	—
287	#3947	C₂³	1	1	yes	characteristic
288	#3947	C₂³	1	1	yes	characteristic
289	#3947	C₂³	1	2	yes	—
290	#3947	C₂³	1	2	yes	—
291	#3946	C₂³	1	2	yes	—
292	#3946	C₂³	1	2	yes	—
293	#3946	C₂³	1	2	yes	—
294	#3946	C₂³	1	2	yes	—
295	#3946	C₂³	1	2	yes	—
296	#3946	C₂³	1	2	yes	—
297	C₈×Dic₅	C₂³	1	2	yes	—
298	C₈×Dic₅	C₂³	1	1	yes	characteristic
299	C₈×Dic₅	C₂³	1	2	yes	—
300	C₈×Dic₅	C₂³	1	1	yes	characteristic
301	C₈×Dic₅	C₂³	1	2	yes	—
302	C₈×Dic₅	C₂³	1	1	yes	characteristic
303	C₈×Dic₅	C₂³	1	1	yes	characteristic
304	C₄⋊#168	C₂³	1	2	yes	—
305	C₄⋊#168	C₂³	1	2	yes	—
306	C₄⋊#168	C₂³	1	1	yes	characteristic
307	C₄⋊#168	C₂³	1	1	yes	characteristic
308	#3935	C₂³	1	1	yes	characteristic
309	#3935	C₂³	1	2	yes	—
310	#3935	C₂³	1	1	yes	characteristic
311	C₄×#168	C₂³	1	2	yes	—
312	C₄×#168	C₂³	1	2	yes	—
313	C₄×#168	C₂³	1	1	yes	characteristic
314	C₄×#168	C₂³	1	1	yes	characteristic
315	#3475	—	5	1	no	—
316	#2971	—	5	1	no	—
317	#2971	—	5	1	no	—
318	#2969	—	5	1	no	—
319	#2969	—	5	2	no	—
320	#2969	—	5	2	no	—
321	#2969	—	5	1	no	—
322	#2967	—	5	2	no	—
323	#2967	—	5	2	no	—
324	#2966	—	5	1	no	—
325	#2966	D₅	1	1	yes	characteristic, complemented
326	#2965	—	5	1	no	—
327	#2965	—	5	1	no	—
328	#2962	—	5	1	no	—
329	#2960	—	5	1	no	—
330	D₄×M₁₆	—	5	1	no	—
331	#2933	—	5	2	no	—
332	#2930	—	5	2	no	—
333	C₂×#436	—	5	1	no	—
334	#2925	—	5	1	no	—
335	#2924	—	5	2	no	—
336	C₄×#131	—	5	1	no	—
337	#2873	—	5	2	no	—
338	C₂³×D₅	C₂²×C₄	1	2	yes	—
339	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
342	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
346	C₂×C₂²⋊D₅	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₂²⋊D₅	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₂²⋊D₅	C₂²×C₄	1	2	yes	—
349	C₂×C₂²⋊D₅	C₂²×C₄	1	2	yes	—
350	C₂×C₂²⋊D₅	C₂²×C₄	1	2	yes	—
351	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
352	#713	—	4	2	no	—
353	D₄×D₅	—	4	2	no	—
354	#709	—	2	2	no	—
355	#709	—	2	2	no	—
356	#709	—	4	2	no	—
357	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
358	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₂₀	C₂²×C₄	1	2	yes	—
360	C₂×C₄×D₅	—	2	4	no	—
361	C₂×C₄×D₅	—	2	4	no	—
362	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
363	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
364	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
365	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
366	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
367	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
368	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
369	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
370	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
371	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
372	C₂×C₄×D₅	C₂⁴	1	2	yes	—
373	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
376	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
377	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
378	C₅×M₁₆	—	2	4	no	—
379	C₂×C₅×C₈	—	2	4	no	—
380	C₂×C₅×C₈	—	2	2	no	—
381	C₂×C₅×C₈	—	2	2	no	—
382	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₅×C₈	C₂⁴	1	2	yes	—
384	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₅×C₈	C₂⁴	1	2	yes	—
386	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
388	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
389	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
390	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
391	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
392	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
393	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
395	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
396	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
397	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
398	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
399	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
401	C₄²×C₅	C₂⁴	1	1	yes	characteristic
402	C₄²×C₅	C₂⁴	1	1	yes	characteristic
403	C₄²×C₅	C₂⁴	1	2	yes	—
404	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
405	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
406	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
407	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
408	C₂²⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
409	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
410	C₂²⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
411	#685	C₂²×C₄	1	2	yes	—
412	#685	C₂²×C₄	1	2	yes	—
413	#685	C₂²×C₄	1	1	yes	characteristic
414	#685	C₂²×C₄	1	1	yes	characteristic
415	#685	C₂²×C₄	1	1	yes	characteristic
416	#685	C₂²×C₄	1	1	yes	characteristic
417	#685	C₂²×C₄	1	2	yes	—
418	#685	C₂²×C₄	1	2	yes	—
419	#685	C₂²×C₄	1	2	yes	—
420	#685	C₂²×C₄	1	2	yes	—
421	#685	C₂²×C₄	1	2	yes	—
422	#685	C₂²×C₄	1	2	yes	—
423	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
424	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
425	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
426	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
427	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
428	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
429	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
430	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
431	#683	C₂²×C₄	1	2	yes	—
432	#683	C₂²×C₄	1	1	yes	characteristic
433	#683	C₂²×C₄	1	1	yes	characteristic
434	#683	C₂²×C₄	1	1	yes	characteristic
435	#683	C₂²×C₄	1	1	yes	characteristic
436	#683	C₂²×C₄	1	2	yes	—
437	#683	C₂²×C₄	1	2	yes	—
438	#683	C₂²×C₄	1	2	yes	—
439	#683	C₂²×C₄	1	2	yes	—
440	#683	C₂²×C₄	1	2	yes	—
441	#683	C₂²×C₄	1	2	yes	—
442	#683	C₂²×C₄	1	2	yes	—
443	C₄×Dic₅	C₂²×C₄	1	2	yes	—
444	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
445	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
446	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
447	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
448	C₄×Dic₅	C₂²×C₄	1	2	yes	—
449	C₄×Dic₅	C₂²×C₄	1	2	yes	—
450	C₄×Dic₅	C₂²×C₄	1	2	yes	—
451	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
452	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
453	C₄×Dic₅	C₂⁴	1	2	yes	—
454	#681	—	2	2	no	—
455	#681	—	2	2	no	—
456	#681	—	2	4	no	—
457	C₂×#168	—	2	4	no	—
458	C₂×#168	C₂⁴	1	2	yes	—
459	C₂×#168	C₂⁴	1	2	yes	—
460	C₂×#168	C₂⁴	1	1	yes	characteristic
461	C₂×#168	C₂⁴	1	1	yes	characteristic
462	C₂×#168	C₂⁴	1	1	yes	characteristic
463	C₂×#168	C₂⁴	1	1	yes	characteristic
464	#676	—	2	4	no	—
465	#676	—	2	2	no	—
466	#676	—	2	4	no	—
467	#676	—	2	2	no	—
468	#676	—	2	4	no	—
469	#676	—	2	4	no	—
470	#676	—	2	2	no	—
471	#676	—	2	4	no	—
472	#676	#41	1	4	yes	complemented
473	C₈×D₅	—	2	2	no	—
474	C₈×D₅	—	2	4	no	—
475	C₈×D₅	—	2	2	no	—
476	C₈×D₅	—	2	2	no	—
477	C₈×D₅	#41	1	4	yes	complemented
478	C₂×#131	—	5	1	no	—
479	C₂×#131	—	5	1	no	—
480	C₂²×M₁₆	—	5	2	no	—
481	C₂²×M₁₆	—	5	2	no	—
482	#556	—	5	1	no	—
483	#555	—	5	1	no	—
484	#554	—	5	1	no	—
485	#553	—	5	2	no	—
486	#552	—	5	2	no	—
487	#552	—	5	1	no	—
488	#552	—	5	1	no	—
489	#551	—	5	2	no	—
490	#551	—	5	2	no	—
491	#547	—	5	1	no	—
492	#546	—	5	1	no	—
493	#546	—	5	1	no	—
494	#533	—	5	1	no	—
495	#529	—	5	1	no	—
496	#529	—	5	2	no	—
497	#529	—	5	2	no	—
498	#529	C₂×D₅	1	1	yes	characteristic
499	#525	—	5	2	no	—
500	C₄×#41	—	5	1	no	—
501	C₄×#41	—	5	1	no	—
502	C₄×#41	—	5	1	no	—
503	C₂×C₄×D₄	—	5	1	no	—
504	C₂×#117	—	5	2	no	—
505	#446	—	5	1	no	—
506	#446	—	5	2	no	—
507	#446	—	5	2	no	—
508	#446	—	5	1	no	—
509	#446	—	5	1	no	—
510	#446	—	5	2	no	—
511	#446	C₂×D₅	1	1	yes	characteristic, complemented
512	C₈×Q₈	—	5	1	no	—
513	C₈×Q₈	—	5	2	no	—
514	C₈×Q₈	—	5	1	no	—
515	C₈×Q₈	—	5	1	no	—
516	C₈×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
517	#436	—	5	2	no	—
518	#436	—	5	1	no	—
519	#436	—	5	2	no	—
520	#436	—	5	1	no	—
521	#436	—	5	1	no	—
522	#436	—	5	2	no	—
523	#436	—	5	2	no	—
524	#436	—	5	2	no	—
525	#436	—	5	2	no	—
526	#436	—	5	2	no	—
527	#436	—	5	1	no	—
528	#436	—	5	2	no	—
529	#436	—	5	1	no	—
530	#436	C₂×D₅	1	1	yes	characteristic
531	#435	—	5	2	no	—
532	#435	—	5	2	no	—
533	#435	—	5	2	no	—
534	#435	—	5	2	no	—
535	#435	—	5	2	no	—
536	#435	—	5	2	no	—
537	#435	—	5	2	no	—
538	#435	—	5	2	no	—
539	#435	—	5	2	no	—
540	#435	C₂×D₅	1	2	yes	complemented
541	C₈×D₄	—	5	1	no	—
542	C₈×D₄	—	5	2	no	—
543	C₈×D₄	C₂×D₅	1	1	yes	characteristic
544	C₈×D₄	C₂×D₅	1	2	yes	complemented
545	#433	—	5	2	no	—
546	#433	—	5	2	no	—
547	#433	—	5	2	no	—
548	#433	—	5	2	no	—
549	#433	—	5	2	no	—
550	#433	C₂×D₅	1	2	yes	complemented
551	#432	—	5	2	no	—
552	#432	—	5	1	no	—
553	#432	—	5	2	no	—
554	#432	C₂×D₅	1	1	yes	characteristic, complemented
555	#431	—	5	1	no	—
556	#431	—	5	2	no	—
557	#431	—	5	1	no	—
558	#431	—	5	2	no	—
559	#424	—	5	2	no	—
560	#424	—	5	2	no	—
561	#423	—	5	1	no	—
562	C₂×C₄⋊C₈	—	5	1	no	—
563	#408	—	5	2	no	—
564	#407	—	5	2	no	—
565	C₂×C₂²⋊C₈	—	5	2	no	—
566	#405	—	5	2	no	—
567	#405	—	5	2	no	—
568	#405	—	5	1	no	—
569	#405	—	5	1	no	—
570	#405	—	5	2	no	—
571	#405	—	5	2	no	—
572	#405	—	5	2	no	—
573	#405	—	5	1	no	—
574	#405	—	5	2	no	—
575	#405	—	5	1	no	—
576	#405	—	5	1	no	—
577	#405	—	5	1	no	—
578	#405	C₂×D₅	1	2	yes	complemented
579	C₄×M₁₆	—	5	1	no	—
580	C₄×M₁₆	—	5	2	no	—
581	C₄×M₁₆	—	5	2	no	—
582	C₄×M₁₆	—	5	2	no	—
583	C₄×M₁₆	—	5	2	no	—
584	C₄×M₁₆	—	5	1	no	—
585	C₄×M₁₆	—	5	1	no	—
586	C₂×C₄×C₈	—	5	1	no	—
587	C₂×C₄×C₈	—	5	1	no	—
588	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
589	C₂³×C₅	C₂³×C₄	1	2	yes	—
590	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
591	C₂²×D₅	—	2	4	no	—
592	C₂²×D₅	—	4	2	no	—
593	C₂²×D₅	—	4	2	no	—
594	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
595	C₂²×D₅	C₂³×C₄	1	2	yes	—
596	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
597	C₅×Q₈	—	2	2	no	—
598	C₅×D₄	—	2	2	no	—
599	C₅×D₄	—	4	2	no	—
600	C₂×C₄×C₅	—	2	2	no	—
601	C₂×C₄×C₅	—	2	2	no	—
602	C₂×C₄×C₅	—	2	1	no	—
603	C₂×C₄×C₅	—	2	1	no	—
604	C₂×C₄×C₅	—	2	2	no	—
605	C₂×C₄×C₅	—	4	1	no	—
606	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
607	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
608	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
609	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
610	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
611	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
612	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
613	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
614	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
615	C₂²⋊D₅	—	2	2	no	—
616	C₂²⋊D₅	—	2	2	no	—
617	C₂²⋊D₅	—	4	2	no	—
618	C₂²⋊D₅	—	4	2	no	—
619	C₂²⋊D₅	—	4	2	no	—
620	C₂×Dic₅	—	2	4	no	—
621	C₂×Dic₅	C₂³×C₄	1	2	yes	—
622	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
623	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
624	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
625	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
626	C₂×Dic₅	C₂³×C₄	1	2	yes	—
627	C₂×Dic₅	C₂³×C₄	1	2	yes	—
628	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
629	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
630	D₂₀	—	2	2	no	—
631	D₂₀	—	2	2	no	—
632	D₂₀	—	4	2	no	—
633	C₄×D₅	—	2	4	no	—
634	C₄×D₅	—	2	2	no	—
635	C₄×D₅	—	2	2	no	—
636	C₄×D₅	—	2	1	no	—
637	C₄×D₅	—	2	1	no	—
638	C₄×D₅	—	2	2	no	—
639	C₄×D₅	—	2	2	no	—
640	C₄×D₅	—	2	4	no	—
641	C₄×D₅	—	4	1	no	—
642	C₄×D₅	—	4	2	no	—
643	C₄×D₅	—	4	2	no	—
644	C₄×D₅	—	4	1	no	—
645	C₄×D₅	—	4	2	no	—
646	C₄×D₅	—	4	2	no	—
647	C₄×D₅	C₂×#41	1	2	yes	—
648	C₄×D₅	C₂×#41	1	2	yes	—
649	Dic₁₀	—	2	2	no	—
650	Dic₁₀	—	2	2	no	—
651	Dic₁₀	—	4	2	no	—
652	C₅×C₈	—	2	1	no	—
653	C₅×C₈	—	2	2	no	—
654	C₅×C₈	—	2	2	no	—
655	C₅×C₈	—	2	1	no	—
656	C₅×C₈	C₂×#41	1	2	yes	—
657	C₅×C₈	C₂×#41	1	2	yes	—
658	#168	—	2	1	no	—
659	#168	—	2	2	no	—
660	#168	—	2	1	no	—
661	#168	—	2	2	no	—
662	#168	C₂×#41	1	2	yes	—
663	#168	C₂×#41	1	2	yes	—
664	C₂×#41	—	5	1	no	—
665	C₂×#41	—	5	1	no	—
666	C₂×#41	—	5	1	no	—
667	C₂²×D₄	—	5	1	no	—
668	C₂³×C₄	—	5	2	no	—
669	#131	—	10	4	no	—
670	#131	—	10	4	no	—
671	C₂×M₁₆	—	5	2	no	—
672	C₂×M₁₆	—	5	1	no	—
673	C₂×M₁₆	—	5	1	no	—
674	C₂×M₁₆	—	5	1	no	—
675	C₂×M₁₆	—	5	2	no	—
676	C₂×M₁₆	—	5	2	no	—
677	C₂×M₁₆	—	5	2	no	—
678	C₂×M₁₆	—	5	2	no	—
679	C₂×M₁₆	—	5	2	no	—
680	C₂×M₁₆	—	5	1	no	—
681	C₂×M₁₆	—	5	1	no	—
682	C₂×M₁₆	—	5	1	no	—
683	C₂×M₁₆	—	10	8	no	—
684	C₂×M₁₆	—	10	8	no	—
685	C₂×M₁₆	C₂²×D₅	1	2	yes	—
686	C₂²×C₈	—	5	1	no	—
687	C₂²×C₈	—	5	2	no	—
688	C₂²×C₈	—	5	2	no	—
689	C₂²×C₈	—	5	1	no	—
690	C₂²×C₈	—	5	1	no	—
691	C₂²×C₈	—	5	1	no	—
692	C₂²×C₈	C₂²×D₅	1	2	yes	—
693	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
694	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
695	C₄⋊Q₈	—	5	1	no	—
696	C₄⋊Q₈	—	5	1	no	—
697	#126	—	5	2	no	—
698	#126	—	5	2	no	—
699	#126	—	5	2	no	—
700	#126	—	5	2	no	—
701	#126	—	5	2	no	—
702	#126	C₄×D₅	1	2	yes	—
703	#125	—	5	2	no	—
704	#125	—	5	2	no	—
705	#125	—	5	1	no	—
706	#125	—	5	2	no	—
707	#125	C₄×D₅	1	1	yes	characteristic
708	#124	—	5	1	no	—
709	#124	—	5	2	no	—
710	#124	—	5	2	no	—
711	#124	C₄×D₅	1	1	yes	characteristic
712	#123	—	5	2	no	—
713	#123	—	5	2	no	—
714	#123	—	5	2	no	—
715	#123	—	5	2	no	—
716	#123	—	5	2	no	—
717	#123	—	5	2	no	—
718	#123	—	5	2	no	—
719	#123	C₄×D₅	1	2	yes	—
720	C₂²⋊Q₈	—	5	1	no	—
721	C₂²⋊Q₈	—	5	2	no	—
722	C₂²⋊Q₈	—	5	1	no	—
723	C₂²⋊Q₈	—	5	2	no	—
724	C₂²⋊Q₈	—	5	2	no	—
725	C₂²⋊Q₈	—	5	1	no	—
726	C₂²⋊Q₈	—	5	2	no	—
727	C₂²⋊Q₈	—	5	2	no	—
728	C₂²⋊Q₈	C₄×D₅	1	1	yes	characteristic
729	#121	—	5	2	no	—
730	#121	—	5	2	no	—
731	#121	—	5	1	no	—
732	#121	—	5	2	no	—
733	#121	—	5	2	no	—
734	#121	C₄×D₅	1	1	yes	characteristic
735	#120	—	5	2	no	—
736	#120	—	5	2	no	—
737	C₄×Q₈	—	5	1	no	—
738	C₄×Q₈	—	5	1	no	—
739	C₄×Q₈	—	5	1	no	—
740	C₄×Q₈	—	5	1	no	—
741	C₄×Q₈	—	5	1	no	—
742	C₄×Q₈	—	5	2	no	—
743	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
744	C₄×D₄	—	5	1	no	—
745	C₄×D₄	—	5	1	no	—
746	C₄×D₄	—	5	1	no	—
747	C₄×D₄	—	5	1	no	—
748	C₄×D₄	—	5	2	no	—
749	C₄×D₄	—	5	1	no	—
750	C₄×D₄	—	5	2	no	—
751	C₄×D₄	—	5	2	no	—
752	C₄×D₄	—	5	2	no	—
753	C₄×D₄	—	5	1	no	—
754	C₄×D₄	—	5	1	no	—
755	C₄×D₄	—	5	2	no	—
756	C₄×D₄	—	5	2	no	—
757	C₄×D₄	—	5	1	no	—
758	C₄×D₄	—	5	1	no	—
759	C₄×D₄	—	5	1	no	—
760	C₄×D₄	—	5	1	no	—
761	C₄×D₄	—	5	2	no	—
762	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
763	C₄×D₄	C₂²×D₅	1	2	yes	—
764	#117	—	5	1	no	—
765	#117	—	5	2	no	—
766	#117	—	5	1	no	—
767	#117	—	5	2	no	—
768	#117	—	5	2	no	—
769	#117	—	5	2	no	—
770	#117	—	5	1	no	—
771	#117	—	5	2	no	—
772	#117	—	5	2	no	—
773	#117	—	5	2	no	—
774	#117	—	5	1	no	—
775	#117	—	5	2	no	—
776	#117	—	5	1	no	—
777	#117	C₂²×D₅	1	2	yes	—
778	C₂×C₄⋊C₄	—	5	2	no	—
779	C₂×C₄⋊C₄	—	5	2	no	—
780	C₂×C₄⋊C₄	—	5	1	no	—
781	C₂×C₂²⋊C₄	—	5	2	no	—
782	C₂×C₂²⋊C₄	—	5	2	no	—
783	C₂×C₂²⋊C₄	—	5	2	no	—
784	C₂×C₄²	—	5	2	no	—
785	C₂×C₄²	—	5	2	no	—
786	C₂×C₄²	—	5	1	no	—
787	C₂×C₄²	—	5	1	no	—
788	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
789	C₄⋊C₈	—	5	2	no	—
790	C₄⋊C₈	—	5	2	no	—
791	C₄⋊C₈	—	5	2	no	—
792	C₄⋊C₈	—	5	2	no	—
793	C₄⋊C₈	—	5	2	no	—
794	C₄⋊C₈	—	5	2	no	—
795	C₄⋊C₈	—	5	1	no	—
796	C₄⋊C₈	—	5	1	no	—
797	C₄⋊C₈	—	5	2	no	—
798	C₄⋊C₈	—	5	2	no	—
799	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
801	C₄⋊C₈	C₂²×D₅	1	2	yes	—
802	C₄⋊C₈	C₂²×D₅	1	2	yes	—
803	C₂²⋊C₈	—	5	2	no	—
804	C₂²⋊C₈	—	5	2	no	—
805	C₂²⋊C₈	—	5	2	no	—
806	C₂²⋊C₈	—	5	2	no	—
807	C₂²⋊C₈	—	5	2	no	—
808	C₂²⋊C₈	—	5	2	no	—
809	C₂²⋊C₈	—	5	2	no	—
810	C₂²⋊C₈	—	5	2	no	—
811	C₂²⋊C₈	—	5	2	no	—
812	C₂²⋊C₈	C₂²×D₅	1	2	yes	—
813	C₂²⋊C₈	C₂²×D₅	1	2	yes	—
814	C₂²⋊C₈	C₂²×D₅	1	2	yes	—
815	#97	—	5	1	no	—
816	#97	—	5	2	no	—
817	#97	—	5	1	no	—
818	#97	—	5	1	no	—
819	#97	—	5	2	no	—
820	#97	—	5	1	no	—
821	#97	—	5	2	no	—
822	#97	—	5	1	no	—
823	#97	—	5	1	no	—
824	#97	—	5	2	no	—
825	#97	C₂²×D₅	1	2	yes	—
826	#97	C₂²×D₅	1	2	yes	—
827	C₄×C₈	—	5	1	no	—
828	C₄×C₈	—	5	1	no	—
829	C₄×C₈	—	5	1	no	—
830	C₄×C₈	—	5	1	no	—
831	C₄×C₈	—	5	2	no	—
832	C₄×C₈	—	5	2	no	—
833	C₄×C₈	—	5	2	no	—
834	C₄×C₈	—	5	1	no	—
835	C₄×C₈	—	5	1	no	—
836	C₄×C₈	—	5	2	no	—
837	C₄×C₈	—	5	2	no	—
838	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
839	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
840	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
841	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
842	C₄×C₈	C₂²×D₅	1	2	yes	—
843	C₂²×C₅	—	2	2	no	—
844	C₂²×C₅	—	2	1	no	—
845	C₂²×C₅	—	2	1	no	—
846	C₂²×C₅	—	2	2	no	—
847	C₂²×C₅	—	2	2	no	—
848	C₂²×C₅	—	2	1	no	—
849	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
850	C₂×D₅	—	2	1	no	—
851	C₂×D₅	—	2	1	no	—
852	C₂×D₅	—	2	2	no	—
853	C₂×D₅	—	2	1	no	—
854	C₂×D₅	—	2	1	no	—
855	C₂×D₅	—	2	2	no	—
856	C₂×D₅	—	2	2	no	—
857	C₂×D₅	—	2	1	no	—
858	C₂×D₅	—	8	4	no	—
859	C₂×D₅	C₄×#41	1	2	yes	—
860	C₄×C₅	—	2	1	no	—
861	C₄×C₅	—	2	2	no	—
862	C₄×C₅	—	2	1	no	—
863	C₄×C₅	—	2	2	no	—
864	C₄×C₅	—	2	2	no	—
865	C₄×C₅	—	2	1	no	—
866	C₄×C₅	—	2	1	no	—
867	C₄×C₅	#568	1	2	yes	—
868	C₄×C₅	C₂²×#41	1	1	yes	characteristic
869	C₄×C₅	C₂²×#41	1	1	yes	characteristic
870	Dic₅	—	2	1	no	—
871	Dic₅	—	2	2	no	—
872	Dic₅	—	2	2	no	—
873	Dic₅	—	2	1	no	—
874	Dic₅	—	2	1	no	—
875	Dic₅	—	2	1	no	—
876	Dic₅	—	2	2	no	—
877	Dic₅	—	2	1	no	—
878	Dic₅	C₄×#41	1	2	yes	—
879	C₂⁴	—	5	2	no	—
880	#41	—	10	2	no	—
881	#41	—	10	2	no	—
882	#41	—	20	2	no	—
883	#41	—	20	2	no	—
884	C₂×Q₈	—	5	1	no	—
885	C₂×Q₈	—	5	1	no	—
886	C₂×Q₈	—	5	2	no	—
887	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
888	C₂×D₄	—	5	1	no	—
889	C₂×D₄	—	5	1	no	—
890	C₂×D₄	—	5	2	no	—
891	C₂×D₄	—	5	2	no	—
892	C₂×D₄	—	5	2	no	—
893	C₂×D₄	—	5	1	no	—
894	C₂×D₄	—	5	1	no	—
895	C₂×D₄	—	5	2	no	—
896	C₂×D₄	—	20	2	no	—
897	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
898	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
899	C₂²×C₄	—	5	1	no	—
900	C₂²×C₄	—	5	2	no	—
901	C₂²×C₄	—	5	1	no	—
902	C₂²×C₄	—	5	1	no	—
903	C₂²×C₄	—	5	2	no	—
904	C₂²×C₄	—	5	2	no	—
905	C₂²×C₄	—	5	2	no	—
906	C₂²×C₄	—	5	1	no	—
907	C₂²×C₄	—	5	1	no	—
908	C₂²×C₄	—	5	2	no	—
909	C₂²×C₄	—	5	2	no	—
910	C₂²×C₄	—	5	2	no	—
911	C₂²×C₄	—	5	2	no	—
912	C₂²×C₄	—	5	1	no	—
913	C₂²×C₄	—	10	4	no	—
914	C₂²×C₄	—	10	4	no	—
915	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
916	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
917	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
918	C₂²×C₄	C₂³×D₅	1	2	yes	—
919	M₁₆	—	2	4	no	—
920	M₁₆	—	5	4	no	—
921	M₁₆	—	10	4	no	—
922	M₁₆	—	10	4	no	—
923	M₁₆	—	10	2	no	—
924	M₁₆	—	10	4	no	—
925	M₁₆	—	10	2	no	—
926	M₁₆	—	10	4	no	—
927	M₁₆	—	10	2	no	—
928	M₁₆	—	10	2	no	—
929	M₁₆	—	10	4	no	—
930	M₁₆	—	10	4	no	—
931	M₁₆	—	10	2	no	—
932	C₂×C₈	—	2	4	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	—	5	1	no	—
936	C₂×C₈	—	5	1	no	—
937	C₂×C₈	—	5	4	no	—
938	C₂×C₈	—	5	1	no	—
939	C₂×C₈	—	5	1	no	—
940	C₂×C₈	—	5	2	no	—
941	C₂×C₈	—	5	2	no	—
942	C₂×C₈	—	10	2	no	—
943	C₂×C₈	—	10	4	no	—
944	C₂×C₈	—	10	2	no	—
945	C₂×C₈	—	10	4	no	—
946	C₂×C₈	—	10	2	no	—
947	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
948	C₂×C₈	C₂³×D₅	1	2	yes	—
949	C₂×C₈	C₂³×D₅	1	2	yes	—
950	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
953	C₄⋊C₄	—	5	1	no	—
954	C₄⋊C₄	—	5	1	no	—
955	C₄⋊C₄	—	5	1	no	—
956	C₄⋊C₄	—	5	2	no	—
957	C₄⋊C₄	—	5	2	no	—
958	C₄⋊C₄	—	5	2	no	—
959	C₄⋊C₄	—	5	2	no	—
960	C₄⋊C₄	—	5	2	no	—
961	C₄⋊C₄	—	5	1	no	—
962	C₄⋊C₄	—	5	1	no	—
963	C₄⋊C₄	—	5	1	no	—
964	C₄⋊C₄	—	5	2	no	—
965	C₄⋊C₄	—	5	2	no	—
966	C₄⋊C₄	—	5	2	no	—
967	C₄⋊C₄	—	5	1	no	—
968	C₄⋊C₄	—	5	1	no	—
969	C₄⋊C₄	—	5	2	no	—
970	C₄⋊C₄	—	5	2	no	—
971	C₄⋊C₄	—	5	2	no	—
972	C₄⋊C₄	—	5	2	no	—
973	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
974	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
975	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
976	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
977	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
978	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
979	C₂²⋊C₄	—	5	2	no	—
980	C₂²⋊C₄	—	5	2	no	—
981	C₂²⋊C₄	—	5	2	no	—
982	C₂²⋊C₄	—	5	1	no	—
983	C₂²⋊C₄	—	5	2	no	—
984	C₂²⋊C₄	—	5	1	no	—
985	C₂²⋊C₄	—	5	2	no	—
986	C₂²⋊C₄	—	5	1	no	—
987	C₂²⋊C₄	—	5	1	no	—
988	C₂²⋊C₄	—	5	2	no	—
989	C₂²⋊C₄	—	5	2	no	—
990	C₂²⋊C₄	—	5	2	no	—
991	C₂²⋊C₄	—	5	2	no	—
992	C₂²⋊C₄	—	5	2	no	—
993	C₂²⋊C₄	—	5	2	no	—
994	C₂²⋊C₄	—	5	1	no	—
995	C₂²⋊C₄	—	5	2	no	—
996	C₂²⋊C₄	—	5	1	no	—
997	C₂²⋊C₄	—	5	2	no	—
998	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
999	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
1000	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
1001	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
1002	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
1003	C₄²	—	5	2	no	—
1004	C₄²	—	5	2	no	—
1005	C₄²	—	5	2	no	—
1006	C₄²	—	5	2	no	—
1007	C₄²	—	5	1	no	—
1008	C₄²	—	5	1	no	—
1009	C₄²	—	5	1	no	—
1010	C₄²	—	5	1	no	—
1011	C₄²	—	5	1	no	—
1012	C₄²	—	5	1	no	—
1013	C₄²	—	5	2	no	—
1014	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
1015	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
1016	C₄²	C₂³×D₅	1	1	yes	characteristic
1017	C₄²	C₂³×D₅	1	1	yes	characteristic
1018	C₄²	C₂³×D₅	1	2	yes	—
1019	C₂×C₅	—	4	2	no	—
1020	C₂×C₅	—	4	1	no	—
1021	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
1022	C₂×C₅	C₂×#568	1	1	yes	characteristic
1023	C₂×C₅	#3573	1	1	yes	characteristic
1024	D₅	—	2	2	no	—
1025	D₅	—	4	1	no	—
1026	D₅	—	4	2	no	—
1027	C₂³	—	5	1	no	—
1028	C₂³	—	5	1	no	—
1029	C₂³	—	5	2	no	—
1030	C₂³	—	10	4	no	—
1031	C₂³	—	20	2	no	—
1032	C₂³	—	20	2	no	—
1033	C₂³	C₂²×C₄×D₅	1	2	yes	—
1034	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
1035	Q₈	—	2	2	no	—
1036	Q₈	—	10	2	no	—
1037	Q₈	—	10	2	no	—
1038	Q₈	—	20	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	10	2	no	—
1042	D₄	—	10	2	no	—
1043	D₄	—	10	2	no	—
1044	D₄	—	10	2	no	—
1045	D₄	—	20	2	no	—
1046	D₄	—	20	2	no	—
1047	D₄	—	20	2	no	—
1048	D₄	—	20	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	5	1	no	—
1056	C₂×C₄	—	5	2	no	—
1057	C₂×C₄	—	5	2	no	—
1058	C₂×C₄	—	5	2	no	—
1059	C₂×C₄	—	5	1	no	—
1060	C₂×C₄	—	5	1	no	—
1061	C₂×C₄	—	5	1	no	—
1062	C₂×C₄	—	5	1	no	—
1063	C₂×C₄	—	5	2	no	—
1064	C₂×C₄	—	5	2	no	—
1065	C₂×C₄	—	5	1	no	—
1066	C₂×C₄	—	10	4	no	—
1067	C₂×C₄	—	10	4	no	—
1068	C₂×C₄	—	10	4	no	—
1069	C₂×C₄	—	10	2	no	—
1070	C₂×C₄	—	10	2	no	—
1071	C₂×C₄	—	10	1	no	—
1072	C₂×C₄	—	10	1	no	—
1073	C₂×C₄	—	10	2	no	—
1074	C₂×C₄	—	10	2	no	—
1075	C₂×C₄	—	20	2	no	—
1076	C₂×C₄	—	20	2	no	—
1077	C₂×C₄	—	20	1	no	—
1078	C₂×C₄	—	20	2	no	—
1079	C₂×C₄	—	20	1	no	—
1080	C₂×C₄	—	20	2	no	—
1081	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1082	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1085	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1086	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1089	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	5	2	no	—
1095	C₈	—	5	2	no	—
1096	C₈	—	10	2	no	—
1097	C₈	—	10	1	no	—
1098	C₈	—	10	2	no	—
1099	C₈	—	10	1	no	—
1100	C₈	D₅×#41	1	2	yes	—
1101	C₈	D₅×#41	1	2	yes	—
1102	C₅	#60217	1	1	yes	characteristic, complemented, Sylow
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	5	2	no	—
1110	C₂²	—	10	1	no	—
1111	C₂²	—	10	1	no	—
1112	C₂²	—	10	2	no	—
1113	C₂²	—	10	1	no	—
1114	C₂²	—	10	1	no	—
1115	C₂²	—	10	2	no	—
1116	C₂²	—	10	2	no	—
1117	C₂²	—	10	1	no	—
1118	C₂²	—	40	4	no	—
1119	C₂²	C₂³×C₄×D₅	1	1	yes	characteristic
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	5	2	no	—
1128	C₄	—	10	2	no	—
1129	C₄	—	10	1	no	—
1130	C₄	—	10	1	no	—
1131	C₄	—	10	1	no	—
1132	C₄	—	10	2	no	—
1133	C₄	—	10	1	no	—
1134	C₄	—	10	2	no	—
1135	C₄	—	10	1	no	—
1136	C₄	#66084	1	2	yes	—
1137	C₄	C₂×D₅×#41	1	1	yes	characteristic
1138	C₄	C₂×D₅×#41	1	1	yes	characteristic
1139	C₂	—	4	2	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	10	2	no	—
1142	C₂	—	20	2	no	—
1143	C₂	—	20	1	no	—
1144	C₂	C₄×D₅×#41	1	1	yes	characteristic
1145	C₂	C₂×#66084	1	1	yes	characteristic
1146	C₂	#10619061	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅
commutator, socle	C₂²×C₅	C₂⁴×C₄
Fitting	C₅×#2966	C₂
prime radical	#10618052	C₂
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	#2966	D₅
hypocenter	C₅	#60217
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #2966

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#2966	C₂	semidirect
3. #10614860	C₂	semidirect
4. #10611689	C₂	semidirect
5. #10611669	C₂	semidirect
6. #10611649	C₂	semidirect
7. #10611636	C₂	semidirect
8. D₅×#436	C₂	semidirect
9. #10611249	C₂	semidirect
10. #10611210	C₂	semidirect
11. #10611187	C₂	semidirect
12. D₄×#676	C₂	semidirect
13. #10611154	C₂	semidirect
14. #10611134	C₂	semidirect
15. #10611134	C₂	semidirect
16. #10611105	C₂	semidirect
17. #10611100	C₂	semidirect
18. #10611065	C₂	semidirect
19. #10611060	C₂	semidirect
20. #10610288	C₂	semidirect
21. #10610279	C₂	semidirect
22. C₄×#4047	C₂	semidirect
23. #10610178	C₂	semidirect
51. C₅×#446	C₂²	semidirect
52. C₅×C₈×Q₈	C₂²	semidirect
54. C₅×#435	C₂²	semidirect
56. C₅×C₈×D₄	C₂²	semidirect
57. C₅×#433	C₂²	semidirect
58. C₅×#432	C₂²	semidirect
59. C₅×#405	C₂²	semidirect
60. C₂×C₄×C₅×C₈	C₂²	semidirect
62. #65416	C₂²	semidirect
63. #65411	C₂²	semidirect
65. #65400	C₂²	semidirect
66. #65400	C₂²	semidirect
67. #65400	C₂²	semidirect
68. #65390	C₂²	semidirect
69. #65390	C₂²	semidirect
70. #65390	C₂²	semidirect
71. #65313	C₂²	semidirect
72. Q₈×#168	C₂²	semidirect
74. #65301	C₂²	semidirect
75. #65300	C₂²	semidirect
77. #65289	C₂²	semidirect
78. #65286	C₂²	semidirect
79. #65214	C₂²	semidirect
80. C₄×#681	C₂²	semidirect
85. #65127	C₂²	semidirect
87. #65125	C₂²	semidirect
88. #65124	C₂²	semidirect
89. #65124	C₂²	semidirect
90. #65122	C₂²	semidirect
91. #65122	C₂²	semidirect
93. #65119	C₂²	semidirect
94. #65119	C₂²	semidirect
95. #65119	C₂²	semidirect
96. #65117	C₂²	semidirect
99. #65018	C₂²	semidirect
100. #65018	C₂²	semidirect
101. #65018	C₂²	semidirect
104. #65014	C₂²	semidirect
106. #65009	C₂²	semidirect
107. #65009	C₂²	semidirect
108. #65009	C₂²	semidirect
109. #64998	C₂²	semidirect
112. #64996	C₂²	semidirect
113. #64996	C₂²	semidirect
114. #64995	C₂²	semidirect
115. #64994	C₂²	semidirect
116. #64990	C₂²	semidirect
120. #64978	C₂²	semidirect
121. #64978	C₂²	semidirect
124. #64977	C₂²	semidirect
126. C₄×#676	C₂²	semidirect
127. C₄×#676	C₂²	semidirect
128. C₄×#676	C₂²	semidirect
129. #64974	C₂²	semidirect
131. C₄×C₈×D₅	C₂²	semidirect
132. #64968	C₂²	semidirect
133. #64968	C₂²	semidirect
134. #64968	C₂²	semidirect
325. #2966	D₅	semidirect
472. #676	#41	semidirect
477. C₈×D₅	#41	semidirect
511. #446	C₂×D₅	semidirect
516. C₈×Q₈	C₂×D₅	semidirect
540. #435	C₂×D₅	semidirect
544. C₈×D₄	C₂×D₅	semidirect
550. #433	C₂×D₅	semidirect
554. #432	C₂×D₅	semidirect
578. #405	C₂×D₅	semidirect
588. C₂×C₄×C₈	C₂×D₅	semidirect
1102. C₅	#60217	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10618052	2
C₅×#2966	2
#10614860	2
#10611689	2
#10611669	2
#10611649	2
#10611636	2
D₅×#436	2
#10611249	2
#10611210	2
#10611187	2
D₄×#676	2
#10611154	2
#10611134	2
#10611105	2
#10611100	2
#10611065	2
#10611060	2
#10610288	2
#10610279	2
C₄×#4047	2
#10610178	2
#60217	5